Number Base Converter

Convert numbers between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Supports arbitrary precision integers, prefix formats (0b, 0o, 0x), negative numbers, and two's complement representation.

Decimal
Hex (Lowercase)
Hex (Uppercase)
Hex (Grouped)
Hex (0x Prefix)
Binary
Binary (Grouped)
Octal
Base64
Two's Complement
Two's Complement (Grouped)

More about Number Bases

Number Systems

A number base (or radix) determines how many unique digits are used to represent numbers. In base N, each digit position represents a power of N.

Base	Name	Digits	Common Use
2	Binary	0, 1	Digital circuits, data storage, bitwise operations
8	Octal	0-7	Unix file permissions, legacy systems
10	Decimal	0-9	Everyday counting, human-readable numbers
16	Hexadecimal	0-9, A-F	Memory addresses, color codes, byte values

Quick Conversion Reference

Decimal	Binary	Octal	Hex
0	0000	0	0
1	0001	1	1
5	0101	5	5
8	1000	10	8
10	1010	12	A
15	1111	17	F
16	10000	20	10
255	11111111	377	FF

Common Prefixes

0b or 0B for binary (e.g., 0b1010 = 10)
0o or 0O for octal (e.g., 0o17 = 15)
0x or 0X for hexadecimal (e.g., 0xFF = 255)

Two's Complement

Two's complement is the standard representation for signed integers in computing. To negate a number: invert all bits, then add 1. In an 8-bit system, values range from -128 (10000000) to 127 (01111111). The most significant bit indicates the sign: 0 for positive, 1 for negative.

Hex in Practice

Colors: #FF5733 = RGB(255, 87, 51). Each pair of hex digits represents one byte (0-255).
Memory: Addresses like 0x7FFF5FBFF8A0 are written in hex because each hex digit maps to exactly 4 binary digits.
File permissions: chmod 755 uses octal. 7 = rwx, 5 = r-x.